Perspective for the Perspective for the measurement of Dmeasurement of D++ v v22 in in the ALICE central barrelthe ALICE central barrel

Elena Bruna, Massimo Masera, Francesco PrinoINFN – Sezione di Torino

ECT*, Heavy Flavour workshop, Trento, September 8th 2006

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Physics motivationPhysics motivation

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Experimental observable: vExperimental observable: v22

....2cos2)cos(212 21

0 RPRP vvXddX

RPv 2cos2

Anisotropy in the observed particle azimuthal distribution due to correlations between the azimuthal angle of the outgoing particles and the direction of the impact parameter

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Sources of charmed meson vSources of charmed meson v22Elliptic flow Collective motion superimposed on top of the thermal motion

Driven by anisotropic pressure gradients originating from the almond-shaped overlap zone of the colliding nuclei in non-central collisions

Requires strong interaction among constituents to convert the initial spatial anisotropy into an observable momentum anisotropy

Probes charm thermalization

IN PLANE

OUT OF PLANE

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Charm flow - 1st ideaCharm flow - 1st idea

Batsouli at al., Phys. Lett. B 557 (2003) 26 Both pQCD charm production without final state effects (infinite mean free

path) and hydro with complete thermal equilibrium for charm (zero mean free path) are consistent with single-electron spectra from PHENIX

Charm v2 as a “smoking gun” for hydrodynamic flow of charm

D from PYTHIAD from Hydro

B from PYTHIA

B from Hydro

e from PYTHIA

e from Hydro

130 GeV Au+Au (0-10%)

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Charm flow and coalescenceCharm flow and coalescenceHadronization via coalescence of constituent quarks successfully explains observed v2 of light mesons and baryons at intermediate pT

hint for partonic degrees of freedomApplying to D mesons: Coalescence of quarks with similar velocities

Charm quark carry most of the D momentumv2(pT ) rises slower for asymmetric hadrons ( D, Ds )

Non-zero v2 for D mesons even for zero charm v2 (no charm thermalization)

Lin, Molnar, Phys. Rev. C68 (2003) 044901

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IN PLANE

OUT OF PLANE

Sources of charmed meson vSources of charmed meson v22Elliptic flow Collective motion superimposed on top of the thermal motion

Driven by anisotropic pressure gradients originating from the almond-shaped overlap zone of the colliding nuclei in non-central collisions

Requires strong interaction among constituents to convert the initial spatial anisotropy into an observable momentum anisotropy

Probes charm thermalization BUT contribution to D meson v2 from the light quark

Parton energy loss Smaller in-medium length L in-

plane (parallel to reaction plane) than out-of-plane (perpendicular to the reaction plane)

Drees, Feng, Jia, Phys. Rev. C71, 034909 Dainese, Loizides, Paic, EPJ C38, 461

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What to learn from vWhat to learn from v22 of D mesons? of D mesons?Low/iterm. pT (< 2-5 GeV/c)

Flow is the dominant effectTest recombination scenarioDegree of thermalization of charm

in the medium Armesto, Cacciari, Dainese, Salgado,

Wiedemann, hep-ph/0511257

Large pT (> 5-10 GeV/c): Energy loss is the dominant

effectTest path-length dependence of in-

medium energy loss in an almond-shaped partonic system Greco, Ko, Rapp PLB 595 (2004) 202

other effects dominant

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Simulation strategy for DSimulation strategy for D++ vv22 in ALICE in ALICE

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Measurement of vMeasurement of v22Calculate the 2nd order coefficient of Fourier expansion of particle azimuthal distribution relative to the reaction plane The reaction plane is unknown.

Estimate the reaction plane from particle azimuthal anisotropy: n = Event plane (n th harmonic) =

estimator of the unknown reaction plane

Calculate particle distribution relative to the event planeCorrect for event plane resolution Resolution contains the unknown RP Can be extracted from sub-events

)](2cos[2 RPv

ii

iin nw

nwn

cossin

tan1 1

)](2cos[' 22 v

RP

vv

2

22 2cos

'

Unknown reaction plane

Event plane resolution

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Motivation and methodMotivation and methodGOAL: Evaluate the statistical error bars for measurements of v2 for D± mesons reconstructed from their K decay

v2 vs. centrality (pT integrated) v2 vs. pT in different centrality bins

TOOL: fast simulation (ROOT + 3 classes + 1 macro) Assume to have only signal Generate ND±(b, pT) events with 1 D± per event For each event

1. Generate a random reaction plane (fixed RP=0)2. Get an event plane (according to a given event plane resolution)3. Generate the D+ azimuthal angle (φD) according to the probability distribution

p(φ) 1 + 2v2 cos [2(φ-RP)]4. Smear φD with the experimental resolution on D± azimuthal angle5. Calculate v′2(D+), event plane resolution and v2(D+)

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DD±± statistics (I) statistics (I)ALICE baseline for charm cross-section and pT spectra: NLO pQCD calculations ( Mangano, Nason, Ridolfi, NPB373 (1992) 295.)

Theoretical uncertainty = factor 2-3 Average between cross-sections obtained with MRSTHO and CTEQ5M

sets of PDF ≈ 20% difference in cc between MRST HO and CTEQ5M

Binary scaling + shadowing (EKS98) to extrapolate to p-Pb and Pb-PbSystem

Pb-Pb(0-5% centr.)

p-Pb (min. bias) pp

sNN 5.5 TeV 8.8 TeV 14 TeVcc

NN w/o shadowing 6.64 mb 8.80 mb 11.2 mb

Cshadowing (EKS98) 0.65 0.80 1.cc

NN with shadowing 4.32 mb 7.16 mb 11.2 mb

Ncctot 115 0.78 0.16

D0+D0bar 141 0.93 0.19D++D- 45 0.29 0.06Ds

++Ds- 27 0.18 0.04

c++c

- 18 0.12 0.02

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DD±± statistics (II) statistics (II)Nevents for 2·107 MB triggersNcc = number of c-cbar pairs MNR + EKS98 shadowing Shadowing centrality

dependence from Emelyakov et al., PRC 61, 044904

D± yield calculated from Ncc Fraction ND±/Ncc ≈0.38

Geometrical acceptance and reconstruction efficiency Extracted from 1 event with

20000 D± in full phase space

B. R. D± K = 9.2 %Selection efficiency No final analysis yet Assume =1.5% (same as D0)

bmin-bmax

(fm) (%) Nevents

(106)Ncc / ev. D±

yield/ev.

0-3 3.6 0.72 118 45.8

3-6 11 2.2 82 31.8

6-9 18 3.6 42 16.3

9-12 25.4 5.1 12.5 4.85

12-18 42 8.4 1.2 0.47

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Event plane simulationEvent plane simulationSimple generation of particle azimuthal angles () according to a probability distribution

Faster than complete AliRoot generation and reconstruction

Results compatible with the ones in PPR chapter 6.4

RPvddN

cos21 2

PPR chap 6.4 Our simulation

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Hadron integrated v2 input values (chosen ≈ 2 RHIC v2)

Ntrack = number of , K and p in AliESDs of Hijing events with b = <b>

Event plane resolution scenarioEvent plane resolution scenarioEvent plane resolution depends on v2 and multiplicity

bmin-bmax <b> Ntrack v2

0-3 1.9 7000 0.02

3-6 4.7 5400 0.04

6-9 7.6 3200 0.06

9-12 10.6 1300 0.08

12-18 14.1 100 0.10

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DD±± azimuthal angle resolution azimuthal angle resolution

From 63364 recontructed D+ 200 events made of

9100 D+ generated with PYTHIA in -2<y<2

Average resolution = 8 mrad = 0.47 degrees

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Simulated results for DSimulated results for D++ v v22

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vv22 vs. centrality vs. centrality

Error bars quite large Would be larger in a scenario with worse event plane resolution May prevent to draw conclusions in case of small anisotropy of D

mesons

bmin-bmax N(D±)selected v2)

0-3 1070 0.024

3-6 2270 0.015

6-9 1900 0.016

9-12 800 0.026

12-18 125 0.09

2·107 MB events

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vv22 vs. p vs. pTT

pT limits N(D±)sel v2)

0-0.5 120 0.06

0.5-1 230 0.05

1-1.5 330 0.04

1.5-2 300 0.04

2-3 450 0.03

3-4 210 0.05

4-8 220 0.05

8-15 40 0.11

pT limits N(D±)sel v2)

0-0.5 140 0.06

0.5-1 280 0.04

1-1.5 390 0.04

1.5-2 360 0.04

2-3 535 0.03

3-4 250 0.05

4-8 265 0.05

8-15 50 0.11

pT limits N(D±)sel v2)

0-0.5 50 0.10

0.5-1 100 0.07

1-1.5 140 0.06

1.5-2 125 0.06

2-3 190 0.05

3-4 90 0.07

4-8 95 0.07

8-15 20 0.15

2·107 MB events

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Worse resolution scenarioWorse resolution scenarioLow multiplicity and low v2

Large contribution to error bar on v2 from event plane resolution

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First conclusions about DFirst conclusions about D++ v v22

Large stat. errors on v2 of D± → K in 2·107 MB eventsHow to increase the statistics? Sum D0→K and D±→K

Number of events roughly 2 → error bars on v2 roughly /√2 Sufficient for v2 vs. centrality (pT integrated)

Semi-peripheral trigger v2 vs. pT that would be obtained from 2·107 semi-peripheral events ( 6<b<9 )pT limits N(D±)sel v2)

0-0.5 645 0.03

0.5-1 1290 0.02

1-1.5 1800 0.017

1.5-2 1650 0.018

2-3 2470 0.015

3-4 1160 0.02

4-8 1225 0.02

8-15 220 0.05

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How to deal with the backgroundHow to deal with the background

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Combinatorial backgroundCombinatorial background

Huge number (≈1010 without PID) of combinatorial Ktriplets in a HIJING central event ≈108 triplets in mass range 1.84<M<1.90 GeV/c2 (D± peak ± 3 )

Final selection cuts not yet defined Signal almost free from background only for pT > 6 GeV/c At lower pT need to separate signal from background in v2

calculation

1 HIJING central event 1 HIJING central event

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First ideas for backgroundFirst ideas for backgroundSample candidate K triplets in bins of azimuthal angle relative to the event plane (φ= φ-2) Build invariant mass spectra of K triplets in φ bins Extract number of D± in φ bins from an invariant mass analysis

Quantify the anisotropy from numbers of D± in the φ bins

x

y

2

D+

φ

φ

Event plane (estimator of the unknown reaction plane)

D meson momentum as reconstructed from the K triplet

produced particles (mostly pions)

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Analysis in 2 bins of Analysis in 2 bins of φφNon-zero v2 difference between numbers of D ± in-plane and out-of-planeExtract number of D± in 90º “cones”: in-plane (-45<φ<45 U 135<φ<225) out-of-plane (45<φ<135 U 225<φ<315)

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Analysis in more bins of Analysis in more bins of φφ16 Δφ binsFit number of D± vs. φ with K[1 + 2v2cos(2φ) ]

0<b<3 3<b<6 6<b<9

v2 values and error bars compatible with the ones obtained from <cos(2φ)>

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Other ideas for backgroundOther ideas for backgroundDifferent analysis methods to provide:

1. Cross checks2. Evaluation of systematics

Apply the analysis method devised for s by Borghini and Ollitrault [ PRC 70 (2004) 064905 ]

Used by STAR for s To be extended from pairs (2 decay products) to triplets (3 decay

products)Extract the cos[2(φ-RP)] distribution of combinatorial K triplets from:

Invariant mass side-bands Different sign combinations (e.g. K+++ and K---)

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BackupBackup

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Flow = collective motion of particles (due to high pressure arising from compression and heating of nuclear matter) superimposed on top of the thermal motion Flow is natural in hydrodynamic language, but flow as intended in heavy

ion collisions does not necessarily imply (ideal) hydrodynamic behaviourIsotropic expansion of the fireball: Radial transverse flow

Only type of flow for b=0 Relevant observables: pT (mT) spectra

Anisotropic patterns: Directed flow

Generated very early when the nuclei penetrate each other– Expected weaker with increasing collision energy

Dominated by early non-equilibrium processes Elliptic flow (and hexadecupole…)

Caused by initial geometrical anisotropy for b ≠ 0– Larger pressure gradient along X than along Y

Develops early in the collision ( first 5 fm/c )

Flow in the transverse planeFlow in the transverse plane

x

y

x

y

z

x

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Ds probe of hadronization: String fragmentation:

Ds+ (cs) / D+ (cd) ~ 1/3

Recombination:Ds

+ (cs) / D+ (cd) ~ N(s)/N(d) (~ 1 at LHC?)Chemical non-equilibrium may cause a shift in relative yields of charmed hadrons:

Strangeness oversaturation (s>1) is a signature of deconfinement

Ds v2 important test for coalescence models Molnar, J. Phys. G31 (2005) S421.

DDss++ K K++KK--++ : motivation : motivation

I. Kuznetsova and J. Rafelski

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Glauber calculations (I)Glauber calculations (I)

mb

mbccNN

inelNN

64.6

60

ABABinelNN

inelAB bTbP )(11)(

)()( bTABbN ABinelNNcoll

)()( bTABbN ABccNNcc

N-N c.s.:

cc from HVQMNR + shadowing

Pb Woods-Saxon

fmdfmrfme

rdrr

549.0624.616.01

)(

0

30

00

32

Glauber calculations (II)Glauber calculations (II) AB

ABinelNN

inelAB bTbb )(112)(

)(2)( bTABbb ABccNN

ccAB

InelPbPb

bc

ccPbPb

bc

bcccPbPb

db

dbN

0

00

mb

mbccNN

inelNN

64.6

60

N-N c.s.:

cc from HVQMNR + shadowing

Pb Woods-Saxon

fmdfmrfme

rdrr

549.0624.616.01

)(

0

30

00

33

Shadowing parametrizationShadowing parametrization

Eskola et al., Eur. Phys. J C 9 (1999) 61. Emel’yanov et al., Phys. Rev. C 61 (2000) 044904.

Rg(x~10-4,Q2=5 GeV2) = 65%from EKS98

),(),(

2

2

QxfQxf

C pg

Pbg

shad

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Why elliptic flow ?Why elliptic flow ?

At t=0: geometrical anisotropy (almond shape), momentum distribution isotropicInteraction among consituents generate a pressure gradient which transform the initial spatial anisotropy into a momentum anisotropy Multiple interactions lead to thermalization

limiting behaviour = ideal hydrodynamic flow

The mechanism is self quenching The driving force dominate at early times Probe Equation Of State at early times

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In-plane vs. out-of-planeIn-plane vs. out-of-plane ....2cos2)cos(21

2 210 RPRP vvX

ddX

Elliptic flow coefficient:v2>0 In plane elliptic flowv2<0 Out of plane elliptic flow

Isotropic

V2=10%V2= - 10%

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More details on vMore details on v22 error bars error bars

bmin-bmax N(D±)selected v2’) RCF RCF) v2) (from v2’ + from RCF)

0-3 1070 0.0213 0.896 0.006 0.024 (= √ (0.0242+ 0.00022)

3-6 2270 0.0148 0.9708 0.0009 0.015 (= √ (0.0152+ 0.000012)

6-9 1900 0.0159 0.9771 0.0007 0.016 (= √ (0.0162+ 0.000032)

9-12 800 0.025 0.971 0.001 0.026 (= √ (0.0262+ 0.000062)

12-18 125 0.061 0.65 0.06 0.09 (= √ (0.092+ 0.0022)

bmin-bmax N(D±)selected v2’) RCF RCF) v2) (from v2’ + from RCF)

0-3 1070 0.022 0.76 0.014 0.029 (= √ (0.0292+ 0.00022)

3-6 2270 0.015 0.934 0.002 0.016 (= √ (0.0162+ 0.000072)

6-9 1900 0.016 0.953 0.002 0.017 (= √ (0.0172+ 0.000062)

9-12 800 0.025 0.934 0.004 0.027 (= √ (0.0272+ 0.00022)

12-18 125 0.061 0.57 0.08 0.11 (= √ (0.1072+ 0.022)

High resolution scenario

Low resolution scenario

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Analysis in 2 bins of Analysis in 2 bins of φφ

Extract number of D± in 90º “cones”: in-plane (-45<φ<45 U 135<φ<225) out-of-plane (45<φ<135 U 225<φ<315)